Phases of the t-J model with random and all-to-all hopping and exchange

We study a t-J model with both t and J random and all-to-all. This model has been studied earlier [1], and can be mapped to an Anderson impurity coupled to self-consistent fermionic and bosonic baths. We employ renormalization group and large M (for models with SU(M) spin symmetry) analyses, and find evidence for a critical non-Fermi liquid phase at zero temperature and small doping. The critical spin correlations are similar to those in a random magnet [2]. A disordered Fermi liquid phase is expected at large doping. We note connections to the physics of the underdoped cuprates.

[1] O. Parcollet and A. Georges, Physical Review B 59, 5341 (1999).
[2] S. Sachdev and J. Ye, Physical Review Letters 70, 3339 (1993).